Jose Abreu still is lumbering around with a walking boot on his left ankle, but could take a a significant step toward his return on Monday.

That's when Abreu is hopeful he'll be able to take off the walking boot and begin participating in some baseball activities with an eye on a June 2 return -- the earliest he could come off the disabled list.

"I don't see a reason why I would have to (miss more time)," Abreu said through team translator Lino Diaz.

Abreu landed on the 15-day disabled list May 18 with posterior tibia tendinitis in his left ankle, an ailment that bothered him for some time before the Sox put him on the shelf. The Sox have exercised caution with their breakout star first baseman, who's hit 15 home runs in 44 games after signing a six-year, $68 million deal in the offseason.

Perhaps the biggest battle is keeping Abreu in good spirits as he'll remain sidelined for at least the next 10 days.

"He's not happy, I know that," manager Robin Ventura said. "When you talk to him you just try to keep it light-hearted and know that for him, he knows we miss him and we'd like him to play as soon as he can. But he needs to be 100 percent. In talking to him, he understands that for him to do what we need to for him to enjoy it he needs to be healthy."

Abreu admitted not playing has been frustrating to the point where he's struggled to watch games now that the White Sox are back in Chicago.

"We have a saying in Spanish, it's hard to see the bulls from far away," Abreu said. "You want to be down there with them. It's very difficult but we're dealing with it the best we can. We're just trying to do everything we can to get back to the field as soon as possible."

When Abreu does return, he expects to make a few tweaks to his daily routine designed to keep him healthy for the rest of the season. One of those tweaks, though, won't be requesting to DH more as he did leading up to being placed on the disabled list.

"We're going to do this the right way so when I'm out there, when I'm playing, I'm able to play on the field," Abreu said. "Obviously, those decisions are meant for the manager, but me personally, I don't like DHing."

It's not an easy balance to strike, with Abreu wanting to get back on the field while needing to sit out 15 days to get back to that point. But it's all part of the larger adjustment period to life in the major leagues -- stints on the disabled list happen, and Abreu's learning how to work through his first one.

"I wish my team could win every time I'm not there," Abreu said. "It is a difficult time."